By Robert L. Tortorelli, Alan Rea, and William H. Asquith


Prepared in Cooperation with the Oklahoma Department of Transportation


This report is also available as a pdf.


U.S. Geological Survey Water-Resources Investigations Report 994232



A regional frequency analysis was conducted to estimate the depth-duration frequency of precipitation for 12 durations in Oklahoma (15, 30, and 60 minutes; 1, 2, 3, 6, 12, and 24 hours; and 1, 3, and 7 days). Seven selected frequencies, expressed as recurrence intervals, were investigated (2, 5, 10, 25, 50, 100, and 500 years). L-moment statistics were used to summarize depth-duration data and to determine the appropriate statistical distributions. Three different rain-gage networks provided the data (15minute, 1-hour, and 1-day). The 60-minute, and 1-hour; and the 24-hour, and 1-day durations were analyzed separately.

Data were used from rain-gage stations with at least 10-years of record and within Oklahoma or about 50 kilometers into bordering states. Precipitation annual maxima (depths) were determined from the data for 110 15-minute, 141 hourly, and 413 daily stations.

The L-moment statistics for depths for all durations were calculated for each station using unbiased L-mo-ment estimators for the mean, L-scale, L-coefficient of variation, L-skew, and L-kur-tosis. The relation between L-skew and L-kurtosis (L-moment ratio diagram) and goodness-of-fit measures were used to select the frequency distributions. The three-parameter generalized logistic distribution was selected to model the frequencies of 15-, 30-, and 60-minute annual maxima; and the three-parameter generalized extreme-value distribution was selected to model the frequencies of 1-hour to 7-day annual maxima.

The mean for each station and duration was corrected for the bias associated with fixed interval recording of precipitation amounts. The L-scale and spatially averaged L-skew statistics were used to compute the location, scale, and shape parameters of the selected distribution for each station and duration. The three parameters were used to calculate the depth-duration-frequency relations for each station. The precipitation depths for selected frequencies were contoured from weighted depth surfaces to produce maps from which the precipitation depth-duration-frequency curve for selected storm durations can be determined for any site in Oklahoma.




Purpose and scope

Previous studies

Climate of Oklahoma


Data base of precipitation annual maxima

Data sources

Correction of precipitation annual maxima for fixed-interval recording

Regionalization of precipitation annual maxima


L-moment ratio diagrams and goodness-of-fit measures

Spatial averaging of L-coefficient of variation and L-skew and estimation of L-scale

Contouring of depth-duration frequency

Depth-duration frequency of precipitation for Oklahoma

Error analysis

Precipitation intensity-duration frequency curve

Comparison to previous studies

Oklahoma Mesonet


Selected references


For sale by U.S. Geological Survey, Information Service

Box 25286, Denver Federal Center

Denver, CO 80224


For more information about the USGS and its products

Telephone: 1-888-ASK-USGS

World Wide Web:

This report is available online in Portable Document Format (PDF). If you do not have the Adobe Acrobat PDF Reader, it is available for free download from Adobe Systems Incorporated.

Download the report (PDF, 44.7MB)

Document Accessibility: Adobe Systems Incorporated has information about PDFs and the visually impaired. This information provides tools to help make PDF files accessible. These tools convert Adobe PDF documents into HTML or ASCII text, which then can be read by a number of common screen-reading programs that synthesize text as audible speech. In addition, an accessible version of Acrobat Reader 5.0 for Windows (English only), which contains support for screen readers, is available. These tools and the accessible reader may be obtained free from Adobe at Adobe Access.


For more information about USGS activities in Oklahoma, visit the USGS Oklahoma District home page.



U.S. Department of the Interior, U.S. Geological Survey
Persistent URL:
Page Contact Information: GS Pubs Web Contact
Last modified: Thursday, September 01 2005, 02:25:42 PM
FirstGov button  Take Pride in America button